> On 16 Mrz., 18:17, fom <fomJ...@nyms.net> wrote:> > >> > > 2) Do you agree that choosing a number from a set with more than 1> > > element means writing or speaking or at least thinking the name of the> > > number?> >> > No. The use of logic and axioms is justifiable as> > representations that formalize mathematical practice.> > The practice must not become unpracticable by logic.

WM is far too often guilt of quantifier dyslexia, a practice not justifiable in mathematics.> > > They are normative ideals against which mathematical> > practice is measured.> > Logic and formalization *describe* practice, they cannot change it.

They can reject such practices as quantifier dyslexia.> > > Your question applies to the faithfulness of those> > representations. What is "nameable in principle" may> > not be materially nameable.> > Here is the question whether something can be chosen, not whether it> can be "in priciple" chosen.> >> > > 5) Zermelo's AC requires that uncountably many names can be written,> > > said or thought.> >> > No. Zermelo's AC requires that one name can be written> > with certainty.> >> > "the cartesian product of non-empty sets is non-empty"> > You could with same ease write: Fermat's last theorem can be violated> with certainty. What would be the difference?

You cannot prove that "Fermat's last theorem can be violated with certainty" follows from assuming thet axiom of choice but one can prove "the cartesian product of non-empty sets is non-empty" follows from assuming thet axiom of choice.

Well maybe WM can't prove it but a mathematician can.> >> > > 6) In this respect it resembles the statement that a second prime> > > number triple beyond (3, 5, 7) can be found, perhaps even infinitely> > > many.> >> > My unfamiliarity with number theory,> > Of six successive naturals, at least two are divisble by 3, one of> them necessarily being an odd one. Therefore there cannot be another> prime triple. But since you refrain from arguing and adhere to> provably false claims, if given the form of axioms, you could also> accept this one.

WM has yet to prove false, by any logic generally acceptable in the mathematical world, that the axiom of choice is false, or prove true that any well ordered set must contain any of his evanescent unfindables whose very existence proves them non-existent.

WM has frequently claimed that a mapping from the set of all infinite binary sequences to the set of paths of a CIBT is a linear mapping.In order to show that such a mapping is a linear mapping, WM must first show that the set of all binary sequences is a vector space and that the set of paths of a CIBT is also a vector space, which he has not done and apparently cannot do, and then show that his mapping satisfies the linearity requirement that f(ax + by) = af(x) + bf(y),where a and b are arbitrary members of a field of scalars and x and y are f(x) and f(y) are vectors in suitable linear spaces.

By the way, WM, what are a, b, ax, by and ax+by when x and y are binary sequences?

If a = 1/3 and x is binary sequence, what is ax ?and if f(x) is a path in a CIBT, what is af(x)?

Until these and a few other issues are settled, WM will still have failed to justify his claim of a LINEAR mapping from the set (but not yet proved to be vector space) of binary sequences to the set (but not yet proved to be vector space) of paths ln a CIBT.

Just another of WM's many wild claims of what goes on in his WMytheology that he cannot back up.--